So the sound cuts out when/if you accidentally bump the tone knob.Just to be sure, I pulled out the input jack, cleaned off the contacts, and checked the control cavity, and all the wires seem to be solidly attached.

So is it just a bad tone pot?

If I unsolder, pop in a new pot, and then solder up exactly as before, will it solve the problem?

if you are lucky, compressed air will do it, but more likely you need something to clean dirt or corrosion off the contacts. i use some stuff i got at radio shack. like this:cleanerjust spray inside the pot where the contacts are, and then spin the knob from end to end a bunch of times, to clean the contact surfaces. it will dry in about a minute or less. then plug it in and check to see if that worked. maybe need to do it a couple times if the pot is really dirty inside. this will fix it most of the time and is much easier than replacing the whole thing.